Banach spaces that admit support sets

Borwein, J.; Vanderwerff, J.

doi:10.1090/S0002-9939-96-03122-X

Banach spaces that admit support sets
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by J. M. Borwein and J. D. Vanderwerff

Proc. Amer. Math. Soc. 124 (1996), 751-755

DOI: https://doi.org/10.1090/S0002-9939-96-03122-X

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Abstract:

It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

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